Sinopsis
A concise exploration of cubic surfaces through classical and projective geometry. This edition presents the general equation of a cubic surface, its tangent planes, and the different kinds of singularities. It also surveys how projective pencils and twisted cubics reveal the surface’s structure, including how many straight lines the surface can contain and how these lines interact with nodes.
The discussion builds from foundational equations to geometric models, connecting algebraic forms to visible shapes. Readers will glimpse methods for constructing and analyzing cubic surfaces, including the role of conic and binode configurations and the behavior of surfaces when lines become imaginary. The text weaves historical references with practical constructions, offering a cohesive view of the subject.
- Understand the general equation of a cubic surface and what triple tangent planes reveal.
- Learn how nodes, binodes, and conic nodes describe the surface’s singularities.
- See how projective pencils and twisted cubics relate to the surface’s lines and sections.
- Explore model-building ideas that link algebra to geometric intuition.
Ideal for readers of advanced geometry, historical treatments of cubic surfaces, and anyone seeking a rigorous, but accessible, pathway into this classical topic.
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Reseña del editor
Excerpt from On Models of Cubic Surfaces
Straight lines meeting three non-intersecting straight lines generate a conicoid, 50. Any one Of the straight lines on a cubic surface is cut by ten others in a range in involution, 51. To place a double six in position, 51 - 54. On the coincidence of straight lines on the surface, 55. Geometrical constructions for placing in position the straight lines on a surface having a conic node, 56. For other nodes, 57, 58. On the number of parabolas on the surface, 59. On the number of points necessary to determine a cubic surface, 61, 62.
About the Publisher
Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Reseña del editor
Excerpt from On Models of Cubic Surfaces
About ten years ago my attention was drawn by a pamphlet of Mr H. M. Taylor to the possibility of arranging the twenty-seven straight lines on a cubic surface in position by geometrical construction, and hence to determine the form of the surface.
After constructing several models, I did not continue the series, for I subsequently found that a complete set had been made in Germany, and had been exhibited by Klein at the Chicago Exhibition. Copies of these models can be purchased.
Still the models described in this book are sufficient to give an idea of the shape of a cubic surface, and to illustrate the changes that take place under certain conditions.
The object of this book is to give an outline of analytical and geometrical methods that are used in treating of cubic surfaces, not taking the more advanced part of the subject, but considering mainly anything that may help to the construction of models.
The latter part of the book is devoted to a description of the shapes of the surfaces.
About the Publisher
Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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On Models of Cubic Surfaces (Classic Reprint)
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Paperback. Condición: New. Print on Demand. This book is a fascinating study of cubic surfaces, a complex geometrical form with a rich history in mathematics. The author provides a comprehensive exploration of the properties of these surfaces, offering a thorough examination of their equations, singularities, and the intricate web of straight lines that lie upon them. The book takes readers on a journey through the development of cubic surfaces, from their early discovery to the present day, showcasing the profound insights and innovative thinking that have shaped our understanding of these captivating mathematical objects. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Nº de ref. del artículo: 9781332337040_0
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On Models of Cubic Surfaces Classic Reprint
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On Models of Cubic Surfaces Classic Reprint
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PAP. Condición: New. New Book. Shipped from UK. Established seller since 2000. Nº de ref. del artículo: LW-9781332337040
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